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In statistics, a moving average (rolling average or running average or moving mean [1] or rolling mean) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. Variations include: simple, cumulative, or weighted forms. Mathematically, a moving average is a type of convolution.
In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. [ 1 ] [ 2 ] The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable.
The notation ARMAX(p, q, b) refers to a model with p autoregressive terms, q moving average terms and b exogenous inputs terms. The last term is a linear combination of the last b terms of a known and external time series . It is given by:
The formula for the MACD line is based on two exponential moving averages of the close prices, usually with the periods of 12 and 26: [5] M A C D l i n e = E M A 12 − E M A 26 {\displaystyle MACD~line=EMA_{12}-EMA_{26}}
Examples of quantitative forecasting methods are [citation needed] last period demand, simple and weighted N-Period moving averages, simple exponential smoothing, Poisson process model based forecasting [15] and multiplicative seasonal indexes. Previous research shows that different methods may lead to different level of forecasting accuracy.
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned ...
To compare money supply and inflation data, we used a 12-month moving average of the year-over-year percentage changes. ... With a 24-month lag, China's annual inflation rate peaked at only 2.1%.
The default Expert Modeler feature evaluates a range of seasonal and non-seasonal autoregressive (p), integrated (d), and moving average (q) settings and seven exponential smoothing models. The Expert Modeler can also transform the target time-series data into its square root or natural log.